Page 276 - Contributed Paper Session (CPS) - Volume 7
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CPS2099 Takatsugu Yoshioka et al.
as (Ni -1)’s tend to infinity. In our derivation, we consider the stochastic
̂
expansions of ̂ and Σ in terms of
Note that the stochastic expansions are derived under = = 0 and
0
Σ = . Then, the Hotelling’s T type statistic can be written as
2
̂
and√ − 2 and ( − 2)Cov( ) can be expanded as
2
respectively. Therefore, the Hotelling’s T type statistic can be expanded as
For details, see Kawasaki and Seo (2016). Using this results and assuming the
standard regularity condition / = (1), = 1,2, we can write
By approximating the distribution of U as
we have
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